24th Annual Meeting(http://mast.queensu.ca/~ssc/ssc96/SSC96e0.html)
WITTKOWSKI, K.M. 24th Annual Meeting(internet-link: "http://mast.queensu.ca/~ssc/ssc96/SSC96e0.html") of the Statistical Society of Canada(internet-link: "http://mast.queensu.ca/~ssc/en/welcome.html") , Waterloo, CA, 02.-05.06.96
When several ordinal variables are known to be correlated monotonously with a given concept (e.g. risk of HIV-infection), both principal component analysis (PCA) and rank tests performed on linear combination of scores (LCS) are inappropriate, because (1) both are not invariant against scale transformations, (2) PCA does not allow for competing risks, (3) LCS relies on subjective postulates about the relative importance of variables (risk factors), and (4) classical rank tests ignore differences in precision among observations [WITTKOWSKI KM The Statistician 38
The procedure of Wittkowski, where (1) rank scores are computed by a scale invariant procedure based on the semi-ordering of the multivariate data (e.g. frequency of different types of contact) only [WITTKOWSKI KM JASA 83 (1988):1163-1170] and (2) these ranks are weighted by 'Fisher information' type-weights [WITTKOWSKI KM JASA 87 (1992):258], is extended to allow for an additional a-posteriori variable (e.g. time until seroconversion) to refine the position of observations within the lattice defined by the a-priori variables.
Knut M. Wittkowski , Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 2G1, Canada, kmw@uwaterloo.ca(kmw@uwaterloo.ca)
WITTKOWSKI, K.M. (1988) Friedman-type statistics and consistent multiple comparisons for unbalanced designs. Journal of the American Statistical Association 83
WITTKOWSKI, K.M. (1989) An asymptotic UMP sign test for discretized data. The Statistician 38
WITTKOWSKI, K.M. (1992) An extension to Wittkowski. JASA 87 :258
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